Some data sets contain data clusters not in all dimension, but in subspaces. Known algorithms select attributes and identify clusters in subspaces. The paper presents a novel algorithm for subspace fuzzy clustering. Each data example has fuzzy membership to the cluster. Each cluster is defined in a certainsubspace, but the the membership of the descriptors of the cluster to the subspace (called descriptor weight) is fuzzy (from interval [0,1]) – the descriptors of the cluster can have partial membership to a subspace the cluster is defined in. Thus the clusters are fuzzy defined in their subspaces. The clusters are defined by their centre, fuzziness and weights of descriptors. The clustering algorithm is based on minimizing of criterionfunction. The paper is accompanied by the experimental results of clustering. This approach can be used for partition of input domain in extraction rule base for neuro-fuzzy systems.
The paper presents the operation of two neuro-fuzzy systems of an adaptive type, intended for solving problems of the approximation of multi-variable functions in the domain of real numbers. Neuro-fuzzy systems being a combination of the methodology of artiﬁcial neural networks and fuzzy sets operate on the basis of a set of fuzzy rules “if-then”, generated by means of the self-organization of data grouping and the estimation of relations between fuzzy experiment results. The article includes a description of neuro-fuzzy systems by Takaga-Sugeno-Kang (TSK) and Wang-Mendel (WM), and in order to complement the problem in question, a hierarchical structural self-organizing method of teaching a fuzzy network. A multi-layer structure of the systems is a structure analogous to the structure of “classic” neural networks. In its ﬁnal part the article presents selected areas of application of neuro-fuzzy systems in the ﬁeld of geodesy and surveying engineering. Numerical examples showing how the systems work concerned: the approximation of functions of several variables to be used as algorithms in the Geographic Information Systems (the approximation of a terrain model), the transformation of coordinates, and the prediction of a time series. The accuracy characteristics of the results obtained have been taken into consideration.